Bare Higgs mass at Planck scale

TL;DR

This paper calculates the quadratic divergences in the bare Higgs mass at high energy scales using two-loop renormalization group equations, finding the scale where the bare mass vanishes near the Planck scale.

Contribution

It provides a detailed computation of the bare Higgs mass divergence at two-loop level and estimates the cutoff scale where it becomes zero, connecting to the hierarchy problem.

Findings

Bare Higgs mass vanishes at about 10^{23} GeV for current top mass

With a slightly lower top mass, the vanishing scale approaches the Planck scale

The cutoff dependence of the bare Higgs mass is explicitly characterized

Abstract

We compute one- and two-loop quadratic divergent contributions to the bare Higgs mass in terms of the bare couplings in the Standard Model. We approximate the bare couplings, defined at the ultraviolet cutoff scale, by the MS-bar ones at the same scale, which are evaluated by the two-loop renormalization group equations for the Higgs mass around 126GeV in the Standard Model. We obtain the cutoff scale dependence of the bare Higgs mass, and examine where it becomes zero. We find that when we take the current central value for the top quark pole mass, 173GeV, the bare Higgs mass vanishes if the cutoff is about 10^{23}GeV. With a 1.3 sigma smaller mass, 170GeV, the scale can be of the order of the Planck scale.